This isn't true, both statistically and it's even reported that Broberg himself hates the right side.
Broberg is actually very strong whenever he plays LD, which is causing me a little bit of pause because he was mostly tossed on the right side. His best performances of the playoffs in the Stars series was on the left side next to Ceci when Kulak moved up to babysit Nurse.
A coaching mistake that doesn't get talked about was moving Kulak down to 3LD and Broberg up to play with Nurse on the account that Kulak doesn't feel comfortable on the right side. The Kulak - Nurse pair was way better than with Broberg, and Broberg played by far his best hockey on the left side on the third pair.